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Theory of the NS-$\overline{\omega}$ model: A complement to the NS-$\alpha$ model

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  • We study a recent regularization of the Navier-Stokes equations, the NS-$\overline{\omega}$ model. This model has similarities to the NS-$\alpha$ model, but its structure is more amenable to be used as a basis for numerical simulations of turbulent flows. In this report we present the model and prove existence and uniqueness of strong solutions as well as convergence (modulo a subsequence) to a weak solution of the Navier-Stokes equations as the averaging radius decreases to zero. We then apply turbulence phenomenology to the model to obtain insight into its predictions.
    Mathematics Subject Classification: 65M12, 65M60, 76D05, 76F65.


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